A novel algorithm to analyze the dynamics of digital chaotic maps in finite-precision domain

doi:10.1088/1674-1056/ac785c

中国物理B ›› 2023, Vol. 32 ›› Issue (1): 10501-010501.doi: 10.1088/1674-1056/ac785c

A novel algorithm to analyze the dynamics of digital chaotic maps in finite-precision domain

Chunlei Fan(范春雷)^† and Qun Ding(丁群)

Electrical Engineering College, Heilongjiang University, Harbin 150080, China

收稿日期:2022-01-02 修回日期:2022-06-12 接受日期:2022-06-14 出版日期:2022-12-08 发布日期:2022-12-20
通讯作者: Chunlei Fan E-mail:2020021@hlju.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 62101178) and the Fundamental Research Funds for the Higher Institutions in Heilongjiang Province, China (Grant No. 2020-KYYWF-1033).

A novel algorithm to analyze the dynamics of digital chaotic maps in finite-precision domain

Chunlei Fan(范春雷)^† and Qun Ding(丁群)

Electrical Engineering College, Heilongjiang University, Harbin 150080, China

Received:2022-01-02 Revised:2022-06-12 Accepted:2022-06-14 Online:2022-12-08 Published:2022-12-20
Contact: Chunlei Fan E-mail:2020021@hlju.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 62101178) and the Fundamental Research Funds for the Higher Institutions in Heilongjiang Province, China (Grant No. 2020-KYYWF-1033).

摘要/Abstract

摘要： Chaotic maps are widely used to design pseudo-random sequence generators, chaotic ciphers, and secure communication systems. Nevertheless, the dynamic characteristics of digital chaos in finite-precision domain must be degraded in varying degrees due to the limited calculation accuracy of hardware equipment. To assess the dynamic properties of digital chaos, we design a periodic cycle location algorithm (PCLA) from a new perspective to analyze the dynamic degradation of digital chaos. The PCLA can divide the state-mapping graph of digital chaos into several connected subgraphs for the purpose of locating all fixed points and periodic limit cycles contained in a digital chaotic map. To test the versatility and availability of our proposed algorithm, the periodic distribution and security of 1-D logistic maps and 2-D Baker maps are analyzed in detail. Moreover, this algorithm is helpful to the design of anti-degradation algorithms for digital chaotic dynamics. These related studies can promote the application of chaos in engineering practice.

关键词: digital chaos, dynamic degradation, state-mapping graph, periodicity analysis

Abstract: Chaotic maps are widely used to design pseudo-random sequence generators, chaotic ciphers, and secure communication systems. Nevertheless, the dynamic characteristics of digital chaos in finite-precision domain must be degraded in varying degrees due to the limited calculation accuracy of hardware equipment. To assess the dynamic properties of digital chaos, we design a periodic cycle location algorithm (PCLA) from a new perspective to analyze the dynamic degradation of digital chaos. The PCLA can divide the state-mapping graph of digital chaos into several connected subgraphs for the purpose of locating all fixed points and periodic limit cycles contained in a digital chaotic map. To test the versatility and availability of our proposed algorithm, the periodic distribution and security of 1-D logistic maps and 2-D Baker maps are analyzed in detail. Moreover, this algorithm is helpful to the design of anti-degradation algorithms for digital chaotic dynamics. These related studies can promote the application of chaos in engineering practice.

Key words: digital chaos, dynamic degradation, state-mapping graph, periodicity analysis

中图分类号: (Low-dimensional chaos)

05.45.Ac

05.45.Gg (Control of chaos, applications of chaos) 05.45.Mt (Quantum chaos; semiclassical methods)

Chunlei Fan(范春雷) and Qun Ding(丁群). A novel algorithm to analyze the dynamics of digital chaotic maps in finite-precision domain[J]. 中国物理B, 2023, 32(1): 10501-010501.

Chunlei Fan(范春雷) and Qun Ding(丁群). A novel algorithm to analyze the dynamics of digital chaotic maps in finite-precision domain[J]. Chin. Phys. B, 2023, 32(1): 10501-010501.

参考文献

[1] Lorenz E N 1963 J. Atmosph. Sci. 20 130
[2] Lahmiri S and Bekiros S 2019 Chaos Solitons & Fractals 118 35
[3] Bayani A, Rajagopal K, Khalaf A J M, Jafari S, Leutcho G D and Kengne J 2019 Phys. Lett. A 383 1450
[4] Argyris A, Pikasis E and Syvridis D 2016 J. Lightw. Technol. 34 5325
[5] Yeoh W Z, The J S and Chern H R 2019 Multimedia Tools and Applications 78 15929
[6] Alcin M, Koyuncu I, Tuna M, Varan M and Pehlivan I 2019 Int. J. Circuit Theory Appl. 47 365
[7] Hu G Z and Li B B 2021 Nonlinear Dyn. 103 2819
[8] Chen B J, Yu S M, Zhang Z Q, Li D D U and Lü J H 2021 Int. J. Bifur. Chaos 31 2150045
[9] Wu X Y and Guan Z H 2007 Phys. Lett. A 365 403
[10] Jamal S S, Shah T and Hussain I 2013 Nonlinear Dyn. 73 1469
[11] Hamza R 2017 J. Inf. Security Appl. 35 119
[12] Pan J, Ding Q and Du B X 2012 Int. J. Bifur. Chaos 22 1250125
[13] Li T Y and Yorke J A 1975 Am. Math. Month. 82 985
[14] Luo Y L, Liu Y Q, Liu J X, Tang S B, Harkin J and Cao Y 2021 Inf. Sci. 556 49
[15] Hu H P, Deng Y S and Liu L F 2014 Commun. Nonlinear Sci. Numer. Simulat. 19 1970
[16] Fan C L and Ding Q 2021 Nonlinear Dyn. 103 1081
[17] Grebogi C, Ott E and Yorke J A 1988 Phys. Rev. A 38 3688
[18] Li S J, Chen G R and Mou X Q 2005 Int. J. Bifur. Chaos 15 3119
[19] Miyazaki T, Araki S, Nogami Y and Uehara S 2011 IEICE Trans. Fund. Electron. Commun. Comput. Sci. E94A 1817
[20] Yin R M, Wang J, Yuan J, Shan X M and Wang X Q 2012 Sci. China Inf. Sci. 55 1162
[21] Yoshioka D and Kawano K 2016 IEEE Transactions on Circuits and Systems II-Express Briefs 63 778
[22] Persohn K J and Povinelli R J 2012 Chaos Solitons & Fractals 45 238
[23] Frahm K M and Shepelyansky D L 2018 Phys. Rev. E 98 032205
[24] Fan C L and Ding Q 2021 Phys. Scr. 96 085212
[25] Zheng J, Hu H P and Xia X 2018 Nonlinear Dyn. 94 1535
[26] Liu Y Q, Luo Y L, Song S X, Cao L C, Liu J X and Harkin J 2017 Int. J. Bifur. Chaos 27 1750033
[27] Fan C L, Ding Q and Tse C K 2022 Int. J. Bifur. Chaos 32 2250075
[28] Bandt C and Pompe B 2002 Phys. Rev. Lett. 88 174102

A novel algorithm to analyze the dynamics of digital chaotic maps in finite-precision domain

A novel algorithm to analyze the dynamics of digital chaotic maps in finite-precision domain

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Guo-Dong Ye(叶国栋), Hui-Shan Wu(吴惠山), Xiao-Ling Huang(黄小玲), and Syh-Yuan Tan. Asymmetric image encryption algorithm based ona new three-dimensional improved logistic chaotic map[J]. 中国物理B, 2023, 32(3): 30504-030504.
[2]	Li-Ping Zhang(张丽萍), Yang Liu(刘洋), Zhou-Chao Wei(魏周超), Hai-Bo Jiang(姜海波), Wei-Peng Lyu(吕伟鹏), and Qin-Sheng Bi(毕勤胜). Extremely hidden multi-stability in a class of two-dimensional maps with a cosine memristor[J]. 中国物理B, 2022, 31(10): 100503-100503.
[3]	Xiaopeng Yan(闫晓鹏), Xingyuan Wang(王兴元), and Yongjin Xian(咸永锦). Synchronously scrambled diffuse image encryption method based on a new cosine chaotic map[J]. 中国物理B, 2022, 31(8): 80504-080504.
[4]	Yan-Mei Lu(卢艳梅), Chun-Hua Wang(王春华), Quan-Li Deng(邓全利), and Cong Xu(徐聪). The dynamics of a memristor-based Rulkov neuron with fractional-order difference[J]. 中国物理B, 2022, 31(6): 60502-060502.
[5]	Li-Ping Zhang(张丽萍), Yang Liu(刘洋), Zhou-Chao Wei(魏周超),Hai-Bo Jiang(姜海波), and Qin-Sheng Bi(毕勤胜). A class of two-dimensional rational maps with self-excited and hidden attractors[J]. 中国物理B, 2022, 31(3): 30503-030503.
[6]	Chunbiao Li(李春彪), Ran Wang(王然), Xu Ma(马旭), Yicheng Jiang(姜易成), and Zuohua Liu(刘作华). Embedding any desired number of coexisting attractors in memristive system[J]. 中国物理B, 2021, 30(12): 120511-120511.
[7]	Qi Li(李琦), Xingyuan Wang(王兴元), He Wang(王赫), Xiaolin Ye(叶晓林), Shuang Zhou(周双), Suo Gao(高锁), and Yunqing Shi(施云庆). A secure image protection algorithm by steganography and encryption using the 2D-TSCC[J]. 中国物理B, 2021, 30(11): 110501-110501.
[8]	Sixiao Kong(孔思晓), Chunbiao Li(李春彪), Shaobo He(贺少波), Serdar Çiçek, and Qiang Lai(赖强). A memristive map with coexisting chaos and hyperchaos[J]. 中国物理B, 2021, 30(11): 110502-110502.
[9]	Xing-Yuan Wang(王兴元), Huai-Huai Sun(孙怀怀), and Hao Gao(高浩). An image encryption algorithm based on improved baker transformation and chaotic S-box[J]. 中国物理B, 2021, 30(6): 60507-060507.
[10]	. [J]. 中国物理B, 2021, 30(2): 20501-0.
[11]	张丽萍, 刘洋, 魏周超, 姜海波, 毕勤胜. A novel class of two-dimensional chaotic maps with infinitely many coexisting attractors[J]. 中国物理B, 2020, 29(6): 60501-060501.
[12]	Adel Ouannas, Amina Aicha Khennaoui, Shaher Momani, Viet-Thanh Pham, Reyad El-Khazali. Hidden attractors in a new fractional-order discrete system: Chaos, complexity, entropy, and control[J]. 中国物理B, 2020, 29(5): 50504-050504.
[13]	王兴元, 张钧荐, 张付臣, 曹光辉. New chaotical image encryption algorithm based on Fisher-Yatess scrambling and DNA coding[J]. 中国物理B, 2019, 28(4): 40504-040504.
[14]	王兴元, 王宇, 王思伟, 张盈谦, 武相军. A novel pseudo-random coupled LP spatiotemporal chaos and its application in image encryption[J]. 中国物理B, 2018, 27(11): 110502-110502.
[15]	董成伟. Topological classification of periodic orbits in Lorenz system[J]. 中国物理B, 2018, 27(8): 80501-080501.